Theorem e33

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e33.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
	e33.2	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )
	e33.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
Assertion	e33	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e33.1	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜃    )
2		e33.2	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜏    )
3		e33.3	⊢ ( 𝜃 → ( 𝜏 → 𝜂 ) )
4	3	a1i	⊢ ( 𝜃 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	1 1 2 4	e333	⊢ (    𝜑    ,    𝜓    ,    𝜒    ▶    𝜂    )